My impression of form factor in the sense of "size, shape, and design of an electronic product" is that it is what Wilson Follett, Modern American Usage (1966) calls a "popularized technicality":
popularized technicalities. ... In our time what is technical and professional is in high repute; what comes from the amateur is regarded as amateurish. Consequently many phrases have been borrowed from the sciences, the techniques, and the professions to adorn and lend expressiveness o ordinary prose. The choice and application of these words and phrases have naturally not been controlled by the experts; the transfer has been indeed amateurish, and examination shows that a good many of the new terms simply duplicate or replace simple words long in use.
Oxford Dictionary of Computing, sixth edition (2008) gives two definitions—one simple and one technical (and difficult)—of the term as used in computer science:
form factor 1. The shape of a piece of equipment expressed either in height, width, and depth, or in terms of a standard item such as a 3½-inch disk drive or a 19-inch rack. 2. The fraction of radiation diffusely emitted from one surface that is received by another. Form factors are used in radiosity calculations and are strictly geometric quantities whose values depend only on the slope and relative location of the surfaces in the scene. Form factors are independent of view and hence do not have to be recomputed for a change of view.
Today, form factor is used extensively in the computer/electronics industry to refer to something like "shape or design [of a product]." At the computer magazines where I worked for many years, some journalists used it constantly in things like cell phone reviews, where (for example) a particular phone would be described as having models were described as having a "clamshell" or a "candybar" or a "slab" form factor. Wikipedia has an entire article on "Form factor (mobile phones)," which begins with this definition:
The form factor of a mobile phone is its size, shape, and style, as well as the layout and position of its major components.
One of the earliest Google Books matches for form factor to use the term as a synonym for size is Jagdish Mehra, The Physicist's Conception of Nature (1973), which nonetheless applies the term to "charged bodies" not to product models:
The result of this more detailed analysis agrees with that of Bloch and Nordsieck except for the observation that the probability of very small energy losses depends on the size (form-factor) of the charged body, in such a manner as to 'render immediate application of real electrons impossible'.
An early instance of equating form factor with shape occurs in C.J. Abend, "Product Appearance as Communication," in Sensory Evaluation of Appearance of Materials: A Symposium (1973):
Another form factor [of a hand ax] is the pointed and wedge shape of the head which is directional and arrow-like in nature; this is a further visual clue with respect to direction of work. The back of the head is blunt, which reveals thickness and heft; massiveness, and potential inertia are made visible.
But the earliest instance that I could find of form factor as a popularized technicality used in connection with a product's size, shape, and design is from an advertisement for four Collins aviation instruments in Flying Magazine (October 1971):
IMPROVED RELIABILITY—At least twice the predicted mean time between failures.
TOP PERFORMANCE—Collins traditional, uncompromised standards of quality.
IDEAL FORM FACTOR—Minimizes rack space; fits previously unusable space in aircraft.
LATEST CAPABILITIES—Full channeling for proposed future requirements.
Here form factor may retain the cachet of its more technical senses in physics, electronics, and elsewhere, but it has lost their complicated meanings. It has become, in short, a ten-cent Madison Avenue term for "size, shape, and/or design."
Update (December 3, 2021): Early newspaper mentions of 'form factor'
An Elephind search for "form factor" turns up instances going back to 1922, although the precise meaning of the term becomes clear only over the course of several years of instances. From "Electricals Announce Thesis Subjects" in the [Cleveland, Ohio] Case Tech (March 1, 1922):
The following are the thesis subjects of the senior electrical students:
"A Study of the Form Factor of Alternating Generators at Low Power Factors." L. F. Radel, M. A. Hyde.
From Alchemist, "Aviation's Debt to Alloys," in the [Perth, Western Australia] West Australian (April 28, 1930):
In considering materials for aircraft construction much importance is attached to the strength-weight factor, which is the result of dividing the ultimate strength in thousands of pounds by the specific gravity. The figure obtained gives, therefore, an expression of the relative amount of strength obtained from an equal weight of different substances. Some strength-weight factors are—alloy steel 19 to 25, duralumin 19, mild steel 7, aluminium 6, Douglas fir 11, spruce 10, oak 8. Stiffness and stability or the "form factor" is another requirement.
From "Radio Oscillating Circuit: Certain Laws Laid Down: Resistance of the Circuit," in the [Adelaide, South Australia] Chronicle (January 8, 1931):
An American radio company, as a result of tests conducted, supplies the curve drawn below, which shows how the resistance of the co[il] varies at radio frequencies, with the size of the wire used. It will be seen that although the gauge is not critical, best results are obtained with a wire size of about 14 gauge. It has been established, then, that for good design of short-wave coils we can use a coil former, any good shellac as a binder, and, if possible, keep the form factor, diameter divided by length, around 1 to 2.5[.] The gauge of wire to suit rigidity, not forgetting the resistance, as shown in the curve.
From "Electric Fundamentals: XXXXIV," in the [Sydney, New South Wales] Catholic Press (July 18, 1935):
The reason for the A.C. milliammeter having a full scale reading of
11 per cent. higher than its D.C. calibration results from the fact that the instrument movement is still giving a deflection which is proportional to the mean value of the current passed through it, and in the case of an A.C. sinusoidal quantity to be measured, the measurement required is the R.M.S. value, which is greater than the mean value. The R.M.S. value bears a constant ratio to the mean value of a sine wave. This ratio is known as the form factor, and has a numerical value of 1.11.
The term thus seems to have originated (in its U.S./Australian incarnation) in electrical engineering, to identify a particular ratio of the root mean square of a sine wave to the wave's mean value—although it also appears at an early date in the context of material stiffness and stability. In a valuable but, regrettably, self-deleted answer, site participant and super-researcher JEL notes nineteenth-century instances of "form factor" that arose in the context of forestry (citations to 1883 and 1895) and electric current (citation to 1896).
The earliest popularized use of "form factor" that the Elephind search turned up was in an advertisement for the Magnavox International Modern television set in the [University Park, Pennsylvania] Daily Collegian (January 17, 1953):
CHECK THESE OTHER MAGNAVOX FEATURES
Optically-filtered Screen; New Superpowered Chassis; New Slanted Sight; High-Fidelity FM Sound; New Slanted Sound; Personalized Tone Control; New Form Factor in Design; Optional Radio-phonograph; Built-in All-Channel UHF Tuned when needed
Although "New Form Factor in Design" may not rank with "New Superpowered Chassis" and "Personalized Tone Control" as an impressive (but vaporous) selling point, you can imagine Mad Men across the highrises of midtown New York clambering to apply it to whatever product they were trying to push. And I'm sure that I speak for consumers everywhere when I say, "If I can't have new slanted sight or new slanted sound, at least give me a new form factor in design."